5/27/2023 0 Comments Slope intercept equation maker![]() Although it is rare for real-world data points to arrange themselves as a perfectly straight line, it often turns out that a straight line can offer a reasonable approximation of actual data. Substituting these values and simplifying the equation, we get, x h and see that the equation is simply the x-coordinate for the x-intercept. Specifying a y-intercept and a slope-that is, specifying b and m in the equation for a line-will identify a specific line. To find the equation of a vertical line having an x-intercept of (h, 0), use the standard form Ax + By C where A 1, B 0, and C is the x-intercept, h. Thus, the slope of this line is therefore 3/1 = 3. In this example, each time the x term increases by 1 (the run), the y term rises by 3. Remember that slope is defined as rise over run the slope of a line from one point to another is the change in the vertical axis divided by the change in the horizontal axis. The m term in the equation for the line is the slope. In this example, the line hits the vertical axis at 9. The reason is that if x = 0, the b term will reveal where the line intercepts, or crosses, the y-axis. As noted above, the b term is the y-intercept. Sometimes, the slope of a line may be expressed in terms of tangent angle such as: m tan. This example illustrates how the b and m terms in an equation for a straight line determine the position of the line on a graph. We can write the formula for the slope-intercept form of the equation of line L whose slope is m and x-intercept d as: y m (x d) Here, m Slope of the line. Now that you know the “parts” of a graph, let’s turn to the equation for a line: The formula for calculating the slope is often referred to as the “rise over the run”-again, the change in the distance on the y-axis (rise) divided by the change in the x-axis (run). The slope tells us how steep a line on a graph is as we move from one point on the line to another point on the line. Technically, slope is the change in the vertical axis divided by the change in the horizontal axis. The other important term to know is slope. The point where two lines on a graph cross is called an intersection point. Similarly, the y-intercept is the value of y when x = 0. You can see the x-intercepts and y-intercepts on the graph above. Mathematically, the x-intercept is the value of x when y = 0. In economics, we commonly use graphs with price (p) represented on the y-axis, and quantity (q) represented on the x-axis.Īn intercept is where a line on a graph crosses (“intercepts”) the x-axis or the y-axis. This is the standard convention for graphs. We will refer to the vertical line on the left hand side of the graph as the y-axis. ![]() Throughout this course we will refer to the horizontal line at the base of the graph as the x-axis. ![]() Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the After identifying the slope and y-intercept from the equation we used them to graph the line. We substituted y = 0 y = 0 to find the x-intercept and x = 0 x = 0 to find the y-intercept, and then found a third point by choosing another value for x x or y y.Įquations #5 and #6 are written in slope–intercept form. These two equations are of the form A x + B y = C A x + B y = C. In equations #3 and #4, both x x and y y are on the same side of the equation. Equations of this form have graphs that are vertical or horizontal lines. Remember, in equations of this form the value of that one variable is constant it does not depend on the value of the other variable. Equation Method #1 x = 2 Vertical line #2 y = 4 Horizontal line #3 − x + 2 y = 6 Intercepts #4 4 x − 3 y = 12 Intercepts #5 y = 4 x − 2 Slope–intercept #6 y = − x + 4 Slope–intercept Equation Method #1 x = 2 Vertical line #2 y = 4 Horizontal line #3 − x + 2 y = 6 Intercepts #4 4 x − 3 y = 12 Intercepts #5 y = 4 x − 2 Slope–intercept #6 y = − x + 4 Slope–interceptĮquations #1 and #2 each have just one variable.
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